A Bernoulli Gibbsian line ensemble $\mathfrak{L} = (L_1, \dots, L_N)$ is the law of trajectories $N-1$ independent random walkers $L_1, L_{N-1}$ with possibly initial and terminal locations that are conditioned to never cross each other or a given up-right path $L_N$ (i.e. $L_1 \geq \cdots L_N$). In this paper we investigate asymptotic behavior sequences ensembles $\mathfrak{L}^N (L^N_1, L^N_N)...

In this work, we evaluate quantum coherence using the $$l_{1}$$ -norm and convex-roof obtain several new results. First, provide some general triangle-like inequalities of coherence, with results better than existing ones. Second, for special three-dimensional states, a method calculating is presented. Lastly, offer distinct upper bounds in measure based on state itself.

Two methods to generate tensor-product Bézier surface patches from their boundary curves and with tangent conditions along them are presented. The first one is based on the tetraharmonic equation: we show the existence and uniqueness of the solution of ∆4−→x = 0 with prescribed boundary and adjacent to the boundary control points of a n× n Bézier surface. The second one is based on the nonhomog...

Let denote the unit circle in the complex plane. Given a function , one uses t usual (harmonic) Poisson kernel for the unit disk to define the Poisson integral of , namely . Here we consider the biharmonic Poisson kernel for the unit disk to define the notion of -integral of a given function ; this associated biharmonic function will be denoted by . We then consider the dilations ...

B.Y. Chen introduced biharmonic submanifolds in Euclidean spaces and raised the conjecture ”Any biharmonic submanifold is minimal”. In this article, we show some affirmative partial answers of generalized Chen’s conjecture. Especially, we show that the triharmonic hypersurfaces with constant mean curvature are minimal. M.S.C. 2010: 58E20, 53C43.

Among various barycentric coordinates and their extensions, the linear and cubic (Hermite) Gordon-Wixom transfinite interpolation schemes deliver the most accurate approximations of the harmonic and biharmonic functions, respectively. However interpolation properties of the original Gordon-Wixom interpolations are studied for convex domains only and, therefore, their current practical importanc...